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# Number Theory/Number Problem

Question

Mountain
This is the second person I have asked for help on this problem, the last expert saw no relation in the numbers hopefully you can give me some advice or clues at the least:
The problem states:
To work it out, read the numbers in pairs whilst looking at the line above...
The picture shows how the numbers are laid out.
What are the next numbers in the sequence

This is an old, and somewhat "cheesy," riddle.

The first line is 3.

Now what do you see? You see one 3.

That gives the second line, 13.

What do you see? You see one 1 and one 3.

That gives the second line, 1113.

Then you see three 1s and one 3.

That gives the third line, 3113.

Then you see one 3, two 1s, and one 3.

That gives 132112.

And so forth...
Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Thank a trillion! So far no one else has been able to answer this... And you did it in LESS THAN 30, even 20! Your the best! I hope you get Volunteer of the Month you deserve it!

Number Theory

Volunteer

#### Clyde Oliver

##### Expertise

I can answer all questions up to, and including, graduate level mathematics. I am more likely to prefer questions beyond the level of calculus. I can answer any questions, from basic elementary number theory like how to prove the first three digits of powers of 2 repeat (they do, with period 100, starting at 8), all the way to advanced mathematics like proving Egorov's theorem or finding phase transitions in random networks. I do not understand why Number Theory is not included in "Advanced Mathematics."

##### Experience

I am a PhD educated mathematician working in research at a major university.

Organizations
AMS

Publications
Various research journals of mathematics. Various talks & presentations (some short, some long), about either interesting classical material or about research work.

Education/Credentials
BA mathematics & physics, PhD mathematics from a top 20 US school.

Awards and Honors
Various honors related to grades, various fellowships & scholarships, awards for contributions to mathematics and education at my schools, etc.

Past/Present Clients
In the past, and as my career progresses, I have worked and continue to work as an educator and mentor to students of varying age levels, skill levels, and educational levels.